Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions. These derivations are then expressed in terms of fundamental constants, elemen...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9970744 |
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| _version_ | 1849407713338982400 |
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| author | Robert Reynolds Allan Stauffer |
| author_facet | Robert Reynolds Allan Stauffer |
| author_sort | Robert Reynolds |
| collection | DOAJ |
| description | In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions. These derivations are then expressed in terms of fundamental constants, elementary, and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers. |
| format | Article |
| id | doaj-art-47605468d3514c00b9eb9c519aba01d3 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-47605468d3514c00b9eb9c519aba01d32025-08-20T03:35:58ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99707449970744Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta FunctionRobert Reynolds0Allan Stauffer1Department of Mathematics and Statistics, York University, Toronto, Ontario M3J1P3, CanadaDepartment of Mathematics and Statistics, York University, Toronto, Ontario M3J1P3, CanadaIn this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions. These derivations are then expressed in terms of fundamental constants, elementary, and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.http://dx.doi.org/10.1155/2021/9970744 |
| spellingShingle | Robert Reynolds Allan Stauffer Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function Journal of Mathematics |
| title | Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function |
| title_full | Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function |
| title_fullStr | Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function |
| title_full_unstemmed | Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function |
| title_short | Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function |
| title_sort | definite integrals involving combinations of powers and logarithmic functions of complicated arguments expressed in terms of the hurwitz zeta function |
| url | http://dx.doi.org/10.1155/2021/9970744 |
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